ABSTRACT

I will present recent work of myself, Andy
Lewis and Mariya Soskova on a reducibility which stems from basic
notions in algorithmic randomness like relative randomness and
lowness for randomness. This was defined by Andre Nies. We develop a
framework for studying the induced degree structure and present
a wide range of results, both local and global. The techniques are an
interesting blend of degree theoretic methods and measure
theoretic arguments.